The recent discovery of the non-Hermitian skin effect has stimulated further research activities [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}. Under the non-Hermitian skin effect, eigenstates of a system become exponentially localized at boundaries, leading to dramatic changes in the system's band and spectral topology [6]}, [7]}, dynamics [15]}, [16]}, [17]}, [10]}, [11]}, [12]}, and spectral symmetry [21]}, [22]}, [23]}. Experimentally, the non-Hermitian skin effect and its consequences have been observed in classical and photonic systems [24]}, [25]}, [26]}, [27]}, as well as in a Bose-Einstein condensate of ultracold atoms [28]}.
In the last case, a dissipative Aharonov-Bohm (AB) chain was implemented in the momentum and hyperfine-spin space of the condensate atoms. As illustrated in Fig. REF , the AB chain consists of a series of triangular AB rings [29]}, each threaded by a synthetic magnetic flux, realized by engineering the phases of the nearest-neighbor hopping rates. Dissipation is introduced through on-site particle loss for each ring, such that dynamics of atoms that remain in the chain is driven by a non-Hermitian Hamiltonian that features non-trivial band topology. Importantly, the interplay of synthetic flux and dissipation gives rise to a non-reciprocal flow in the bulk that lies at the origin of the non-Hermitian skin effect.
In the experiment, the non-Hermitian skin effect was observed through a directional propagation of atoms along the chain, while the topological edge states were probed through an inverse spectroscopy, where atoms are injected into an empty dissipative AB chain from a bystander state.
Despite its experimental implementation, a systematic study of the topological properties of the dissipative AB chain is missing in the literature.
Further, given the intrinsic difficulty of detecting topological edge states in the presence of non-Hermitian skin effects (as both are localized at the boundary), more variety of detection schemes is desirable.
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